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Markov Encoding for Detecting Signals
in Genomic Sequences
Jagath C. Rajapakse and Loi Sy Ho
Abstract—We present a technique to encode the inputs to neural networks for the detection of signals in genomic sequences. The
encoding is based on lower-order Markov models which incorporate known biological characteristics in genomic sequences. The
neural networks then learn intrinsic higher-order dependencies of nucleotides at the signal sites. We demonstrate the efficacy of the
Markov encoding method in the detection of three genomic signals, namely, splice sites, transcription start sites, and translation
initiation sites.
Index Terms—Genomic sequences, gene structure prediction, Markov chain, neural networks, splice sites, transcription start site,
translation initiation site.
æ
1
INTRODUCTION
L
IVING organisms
carry genetic information in the form of
DNA molecules. Recent advances in DNA sequencing
technology have led to an explosion of genomic data.
Information in cells passes from DNA to mRNA to proteins
through processes called transcription and translation. Each
DNA molecule contains genes which decide the structural
components of cells, tissues, and enzymes for biochemical
reactions essential for its survival and functioning. In the
process of transcription, genes in the DNA sequences are
converted into corresponding mRNA sequences. In the
process of translation, the nucleotides in the coding regions
are translated to synthesize proteins. In eukaryotic genomes, a gene is structured by a variety of biological features,
such as promoter, start codon, introns, exons, splice sites,
and stop codon.
Signals in genomic sequences refer to specific sites or small
sequence segments that are directly related to transcription
and translation processes or to their regulation. This paper
deals with computational techniques that identify signals in
genomic sequences. Knowledge of the presence of signals in
genomic sequences gives insight into transcription and
translation processes and the location and annotation of
genes, that are vital to the investigations of novel and effective
drugs having minimal side effects. We address two important
problems in signal detection, how to automatically identify
the transcription start sites (TSS) and recognize the translation
initiation sites (TIS) in eukaryotic DNA sequences, and
another important problem in gene annotation: the determination of intron and exon boundaries or splice sites (SS).
Bioinformatics approaches for automatic annotation of
genomic sequences have recently gained increased attention
because of the capital-intensive and time-consuming nature
of pure experimental approaches.
. The authors are with the BioInformatics Research Center, School of
Computer Engineering, Nanyang Technological University, Singapore
639798. E-mail: [email protected], [email protected].
Manuscript received 31 Aug. 2004; revised 29 Nov. 2004; accepted 13 Dec.
2004; published online 2 June 2005.
For information on obtaining reprints of this article, please send e-mail to:
[email protected], and reference IEEECS Log Number TCBBSI-0103-0804.
1545-5963/05/$20.00 ß 2005 IEEE
1.1 Motivation
Though many attempts have been made to localize signals
with appropriate models and algorithms, using genetic
contexts, every technique has its own limitations and
drawbacks [33]. Accurate detection of regulatory signals,
such as SS, TSS, or TIS, needs to take into account the
underlying relationships among nucleotides or features
surrounding them. Though the potential of higher-order
Markov models has been touted to represent complex
interactions among genomic sequences, their implementation has become practically prohibitive because of the need
for the estimation of large numbers of parameters [18]. The
neural network approaches, on the other hand, are capable
of discriminating intrinsic patterns in the vicinity of signals
by finding appropriate non-linear mapping. The networks
that receive low-level inputs, e.g., a string of nucleotides, do
not employ explicit sequence features of biological significance. Combining the probabilistic and neural network
approaches in a sensible way would lead to more efficient
approaches in modeling and detecting signals.
This paper introduces the Markov/neural hybrid approach to signal detection by introducing a novel encoding
scheme for inputs to neural networks, using lower-order
Markov chains. The lower-order Markov models incorporate biological knowledge differentiating the compositional
properties of the regions surrounding the signals; the neural
networks combine the outputs from Markov chains, which
we refer to as Markov encoding of inputs, to derive longrange and complex interactions among nucleotides, that
improve the detection of signals. We will demonstrate the
ability and efficacy of our approach in the detection of SS,
TSS, and TIS. The significant improvements of the accuracies achieved for signal detection with Markov encoding
would suggest that the lower-order Markov chains correctly
represent the input features relevant to biological phenomena and the proposed Markov/neural hybrid systems have
the potential for representing complex signals in genomic
sequences.
Published by the IEEE CS, CI, and EMB Societies & the ACM
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2
IEEE/ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS,
PREVIOUS APPROACHES FOR SIGNAL DETECTION
2.1 Splice Sites (SS)
Considering 5’/3’ direction, a donor site is the SS at the 5’
end and an acceptor site is the SS at the 3’ end of an intron.
The splicing machinery needs to recognize and remove
introns to make the correct message for protein production,
yielding the importance of locating the SS in genomic
sequences. SS have some distinct characteristics; one such
characteristic is the “AG-GT” rule that an acceptor site has a
conserved AG di-nucleotide and a donor site has a
conserved GT di-nucleotide. An exception to this rule is
found in a small handful of cases which have AC and AT
di-nucleotides at either end of the sites instead [4].
Unfortunately, the detection of SS is often complicated
because of common occurrences of consensus di-nucleotides at sites other than the SS.
Various computational techniques and algorithms have
recently been developed for SS detection: neural network
approaches [4], [11], [14], [29], [34], probabilistic models [6],
[26], [38], and techniques based on discriminant analysis [39].
These methods primarily seek consensus motifs or features
surrounding the SS by deriving a priori models from training
samples [16]. Neural networks attempt to recognize the
complex features of the neighborhood surrounding the
consensus di-nucleotides by learning an intrinsic nonlinear
transformation [4], [11], [14], [29], [34]. Probabilistic models,
in a different way, estimate position-specific probabilities of
nucleotides at the SS by computing likelihoods of the
candidates of signal sequences [6], [26], [38]. The discriminant
analysis uses several statistical measures to evaluate the
presence of specific nucleotides, allowing recognition of the
SS without explicitly determining their probability distributions [39]. Additionally, postprediction rule-based filtering
techniques have often been performed empirically to enhance
the performance of the prediction [14], [16]. Though a
substantial number of techniques have been reported in
recent literature, the accuracy of SS detection has not yet been
satisfactory enough [10], [23], [35].
2.2 Transcription Start Sites (TSS)
A promoter is a region centered around a TSS which is
biologically the most important signal controlling and
regulating the initiation of the transcription of the gene
immediately downstream [40]. A gene has at least one
promoter [9]. Promoters have very complex sequence
structures, reflecting the complicated protein-DNA interactions during which various transcription factors (TF) are
bound [1]. They can be dispersed or overlapped, largely
populating in about 1 Kbp region upstream and surrounding the TSS. Their functions can be either positive or
negative and are often context-dependent. Eukaryotes have
three different RNA-polymerase promoters that are responsible for transcribing different subsets of genes: RNApolymerase I promoters transcribe genes encoding ribosomal RNA, RNA-polymerase II promoters transcribe genes
encoding mRNA and certain small nuclear RNAs, and RNA
polymerase III promoters transcribe genes encoding tRNAs
and other small RNAs [25]. The present work focuses on
detecting TSSs in RNA polymerase II promoters whose
regulation is the most complex of the three types.
The typical structure of a polymerase II promoter is
approximately located in the region ½50; þ50 with respect
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to the TSS and contains multiple binding sites that occur in
specific contexts. The TF binding sites are typically 5-15 bp
long [9], [25]. The nucleotide specificity at different
positions within the sites varies. A TATA box, a binding
site usually found at -25 bp upstream of the TSS in
metazoans, is the most conserved sequence motif in the
core region [7]. Around the TSS, there is a loosely conserved
initiator region, abbreviated by Inr, which overlaps with
TSS. The Inr is a much weaker signal compared to the
TATA box, but also an important determinant of promoter
strength. In the absence of TATA box, the Inr could
determine the location of the TSS [9]. Also, there exist
many regions giving exact matches to the TATA box and
the Inr which do not represent the true promoter regions.
In spite of a number of computational techniques and
algorithms developed for promoter recognition, only the
applications of probabilistic models [7], [21], [22] and neural
networks [30] have reported a fair degree of success [9]. As
the promoter activity depends closely on how different TFs
bind to the promoter region, in principle, the binding sites
can be determined by looking at the contextual dependencies of the nucleotides. Neural networks attempt to
recognize the complex features of the neighborhood
surrounding the TSS by learning the arbitrary nonlinear
transformations [30]. Probabilistic models, in a different
way, focus on the homology search in the vicinity of the
promoter by estimating position-specific probabilities of
elements [1]. An evolutionary algorithm evolving straightforward motifs in the promoter region has recently been
applied to locate potentially important patterns by inspection [7]. One can alternatively combine modules recognizing individual binding sites by using some overall
description on how these sites are spatially arranged [9].
2.3 Translation Initiation Sites (TIS)
The beginning of the coding region of a gene is marked by a
TIS, most of which contain a conserved triplet of nucleotides ATG, or the start codon, while a few exceptions are
reported in eukaryotes [12], [24], [37]. At the first stage of
the translation process, a small subunit of ribosome binds at
the capped 5’-end of the mRNA and subsequently scans
through the sequence until the first ATG in appropriate
context is encountered [17]. The first occurrence of triplet
ATG in the sequence may not always be chosen for
translation as in approximately 40 percent of cases, an
ATG further downstream is reported to be selected [24]. The
TIS detection becomes more complex when using unannotated genomes that are not fully understood or analyzing
expressed sequence tags which usually contain errors [18].
Analyses to uncover underlying features in the vicinity
of TIS that are important for discovering true sites have
been explored by using a number of computational
techniques and algorithms. From a weight matrix estimated
on an extended collection of data, Kozak [17] derived the
consensus motif gccaccAT Gg, in which the position þ4
(nucleotide G) and position 3 (nucleotide A) are highly
conserved and exert the strongest effect, assuming that +1 is
the position of nucleotide A of the conserved triplet ATG.
This result was later enhanced by Pedersen and Nielsen [24]
when they trained a feedforward multilayer neural network
with input windows of 203 nucleotides centered at the ATG,
except for one disregarded position, and revealed that
position 3 is crucial for TIS recognition. They also
RAJAPAKSE AND HO: MARKOV ENCODING FOR DETECTING SIGNALS IN GENOMIC SEQUENCES
133
Fig. 1. The representation of a splice site by a signal segment and upstream segment and downstream segments of DNA: (a) acceptor site and
(b) donor site.
discovered that ATGs that are in-frame to the TIS are more
likely to be predicted incorrectly as TIS regardless of
whether they are upstream or downstream of the start
codon. Hatzigeorgiou developed an integrated method by
combining a consensus neural network sensitive to the
conserved motif and a coding neural network sensitive to
the coding-noncoding potential around the start codon,
with a ribosome scanning model [12]. While the consensus
neural network assesses a window of nucleotides from
position -7 to +5 relative to the triplet ATG, the coding
neural network working on a window of 54 nucleotides
applies to the codon usage statistic. Salamov et al. [31]
showed that the most important component for the correct
identification is the positional triplet weight matrix around
conserved triplet ATG and the hexanucleotide difference
before and after the ATG in a window of 50 bases long. The
results of the locality-improved kernel in Zien et al. [41]
over that of standard polynomial kernels suggested that the
local correlations are more important than long-range
correlations in identifying TIS. Wong et al. [18], [37]
proposed a data mining tool comprised of generating and
selecting explicit features and integrating the selected
features for decision making; their work found nine
relevant features.
3
MODELS
OF
SIGNALS
3.1 Markov Models of DNA Sequences
Segments of genomic sequences are often modeled by
Markov models whose observed state variables are elements
drawn from the alphabet DNA of four bases: A, T, G, and C.
The Markov chain is defined by a number of states, equal to
the number of nucleotides in the sequence, where each state
variable of the model corresponds to a nucleotide. Consider a
sequence ðs1 ; s2 ; . . . sl Þ of length l, modeled by a Markov
chain, where the nucleotide si 2 DNA is a realization of the
ith state variable of the Markov chain. Except from state i to
state i þ 1, there is no transition from state i to the other states.
The model serially travels from one state to the next while
emitting letters from the alphabet DNA in which each state is
characterized by a position-specific probability parameter. In
previous work [1], [6], [32], the Markov chain model is
referred to as weight array matrix model.
If the Markov chain, say M, has an order k, the likelihood
of the sequence is given by
P ðs1 ; s2 ; . . . sl jMÞ ¼
l
Y
Pi ðsi Þ;
ð1Þ
i¼1
where the Markovian probability Pi ðsi Þ ¼ P ðsi jsi1 ; si2 ;
. . . sik Þ denotes how conditionally the appearance of the
nucleotide at location i depends on its k predecessors. In case
i k, lower-order dependencies should appropriately be
used. Such a model is characterized by a set of parameters,
fPi ðsi jsi1 ; . . . ; sik Þ : si ; si1 ; . . . sik 2 DNA ; i ¼ 1; 2; . . . ; lg.
That is, we need to maintain 4kþ1 parameters at each state to
represent the segment.
3.2 Model of SS
The SS model is considered as a concatenation of three
consecutive DNA segments: signal segment (S S ), upstream
segment (S U ), and downstream segment (S D ), as illustrated in
Fig. 1. The signal segment representing the consensus pattern
responsible for splicing mechanism consists of nucleotides
immediately neighboring the SS. The upstream and downstream segments adjoining the signal segment on both sides
capture the features and contrast of the coding and noncoding
sequences. If the length of the signal segment of the sequence
at SS is lS and the lengths of the upstream and downstream
segments are lU and lD , respectively, the model of the splice
site is represented by a sequence of length lU þ lS þ lD . For the
selection of the values of the lengths of these segments, the
reader is referred to [4], [6], [26].
The three segments in the model of SS are represented by
three Markov chains and a feedforward multilayer neural
network receiving the Markovian probabilities as inputs.
The Markovian probabilities are concatenated as illustrated
in Fig. 2 and fed to the network with n input nodes:
n ¼ lU þ lS þ lD . If the input to the jth input node of the
network is xj ,
8 U
P ðs Þ; if j lU and i ¼ j;
>
>
> iS i
>
< Pi ðsi Þ; if lU j < lU þ lS
ð2Þ
xj ¼
and i ¼ j lU ;
>
>
>
PiD ðsi Þ; if lU þ lS j < lU þ lS þ lD
>
:
and i ¼ j lU lS :
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Fig. 2. Splice site prediction: The outputs of lower-order Markov models representing the three segments are processed by a multilayer neural
network.
A first-order Markov chain is used to represent the
consensus segment of the signal and second-order Markov
chains are used to represent the upstream and downstream
segments. The neural network combines the lower-order
interactions of nucleotides, given by the Markov models,
nonlinearly, to capture any relevant higher-order contextual
information for SS prediction. Accordingly, the present
hybrid model allows the incorporation of biological
information as well as intrinsic distant interactions of
nucleotides.
3.3 Model of TSS
The model of TSS is represented by a promoter of length
100 bp ½50; 50, presuming that the candidate TSS position
starts at þ1. The promoter consists of two sequence
segments, as illustrated in Fig. 3: the TATA-box segment,
a subsequence of 30 bp from 40 to 10, and the Inr
segment, a subsequence of 25 bp from 14 to 11. The
segment sizes are selected so that the consensus motifs for
both binding sites are included. For information on the
rationale for the selection of the configuration of these
segments, the reader is referred to [1], [22], [30]. There are
three independent Markov chains modeling the TATA-box
segment, the Inr segment, and the concatenation of the
TATA-box and Inr segments. The concatenated segment
allows long-range interactions between both sides of the
TSS. A second-order is chosen for the TATA-box model
while the first-order is chosen for the Inr model because of
the weak consensus of the Inr segment [9].
The outputs of the Markov chains are processed by three
parallel neural networks working in cascade, as illustrated
in Fig. 4. The orthogonal coding of DNA sequences has
often been used at the inputs of neural networks, which
encodes each nucleotide si by four binary digits, say bsi ,
where only one digit is set to 1 and the remaining digits are
set to 0, for instance: bA ¼ ð1; 0; 0; 0Þ, bC ¼ ð0; 1; 0; 0Þ,
bG ¼ ð0; 0; 1; 0Þ, and bT ¼ ð0; 0; 0; 1Þ. Given a sequence
ðs1 ; s2 ; . . . ; sl Þ of length l, where si 2 DNA , the orthogonal
coding results in a vector ðbs1 ; bs2 ; . . . ; bsl Þ representing
4l number of inputs to the neural network. The Markov
encoding combines the Markovian probability parameters
with the orthogonal coding: the input sequence results in a
vector ðcs1 ; cs1 ; . . . ; csl Þ of inputs to the neural network
where csi ¼ Pi ðsi Þbsi , for 1 i l. The Markov encoding
thereby incorporates the homology of potential promoter
regions, given by the Markov models, into the neural
network-based approaches.
3.4 Model of TIS
The TIS model consists of three parts: conserved ATG
triplet, an upstream segment, and a downstream segment,
as illustrated in Fig. 5. The upstream segment consists of
50 nucleotides, from 50 to 1, and the downstream
segment consists of 50 nucleotides, from þ4 to þ53,
assuming that þ1 is the position of the first nucleotide A
of the candidate ATG. For the selection of the width of these
segments, the reader is referred to [18], [24], [31], [41]. As
the TIS without the conserved triplet ATG is reported to be
rare in eukaryotes [37], such cases are not addressed here.
Fig. 3. The representation of the transcription start site (TSS) by a promoter consisting of a TATA-box and an Inr segment.
RAJAPAKSE AND HO: MARKOV ENCODING FOR DETECTING SIGNALS IN GENOMIC SEQUENCES
135
Fig. 4. Transcription start site (TSS) prediction: The outputs of three Markov chain models, representing the TATA-box segment, the concatenation
of TATA-box and Inr segment, and Inr segment, are processed by three neural networks whose outputs are combined with a voting scheme.
Fig. 5. The representation of a translation initiation site (TIS) by a conserved triplet, ATG, and upstream and downstream segments.
Two independent Markov chains model the upstream
and downstream segments. Due to weak dependencies of
the nucleotides in the noncoding region [32], the first-order
is chosen for the upstream model while, in an attempt to
capture codon distributions, the second-order is chosen for
the downstream model. The output Markov probabilities
are combined with orthogonal encoding in a manner similar
to that used for input coding in the TSS detection. In a real
eukaryotic genome, the possibility of a true TIS signal
without a conserved triplet ATG is much lower than the
possibility of a true SS without a conserved di-nucleotide.
Therefore, we decided to avoid ATG start codon in the
concatenation of the upstream and downstream segments.
The downstream segment is further represented by a
protein encoding technique based on a coding differential
analysis [6], [12], [32]. In order to account for a coding
measure in the downstream region, the protein encoding
model transforms the DNA sequence to a vector of
38 elements by applying Percent Accepted Mutation
(PAM) matrices [8]. The nucleotide sequences are first
converted into amino acid sequences and then the amino
acids are grouped into six exchange groups, representing
conservative replacements through evolution [36]; the
36 elements of the vector give normalized frequencies of
the corresponding di-exchange symbols and the last two
elements track the presence of stop codon in the downstream segment. Previous investigations have shown that
the coding differential method is effective in distinguishing
coding from noncoding regions [6], [12], [32].
The outputs from Markov chains of upstream and
downstream segments and the protein coding model for
downstream segments are processed by three feedforward
neural networks, as illustrated in Fig. 6. The outputs of
three neural networks are combined using a majority voting
scheme for the prediction. The approach searches the TIS in
the DNA sequence until at least two of three neural
networks predict truly. Once the first suitable ATG is
detected as the correct TIS, the present method stops
scanning the DNA sequence for another TIS as in the
ribosome scanning model [12].
4
HIGHER-ORDER MARKOV MODEL
OF
SIGNALS
4.1 Neural Networks
The neural networks used in the models were multilayer
perceptron (MLP). If an MLP network has n input nodes,
one hidden-layer of m neurons, and one output neuron, the
output of the network is given by
!!
m
n
X
X
;
ð3Þ
y¼f
wk fk
wkj xj
k¼1
j¼1
where fk ; k ¼ 1; 2; . . . ; m, and f denote the activation functions of the hidden-layer neurons and the output neuron,
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Fig. 6. Translation initiation site (TIS) prediction: The outputs of the upstream and downstream Markov chain models and the downstream protein
encoding model are processed by three neural networks whose outputs are combined in a voting scheme.
respectively; wk ; k ¼ 1; 2; . . . m and wkj ; k ¼ 1; 2; . . . m; j ¼
1; 2; . . . n denote the weights connected to the output neuron
and to the hidden-layer neurons, respectively. The output
activation function was selected to be a unipolar sigmoidal:
fðuÞ ¼ =ð1 þ eu Þ and the hidden-layer activation functions took the form of hyperbolic tangent sigmoidals:
fk ðuÞ ¼ k ðek u ek u Þ=ðek u þ ek u Þ, for all k. The weights
of the networks were learned with the standard backpropagation algorithm [13].
4.2 Higher-Order Markov Models of Signals
Lower-order Markov chains provide a means of incorporating the characteristics of coding and noncoding regions by
linearly modeling interactions among neighboring nucleotides. The neural networks in our approach receive
Markovian probabilities and combine them nonlinearly in
order to learn more complex and distant interactions among
nucleotides. In what follows, we show that, indeed, such
lower-order Markov/neural hybrid models result in higherorder Markov models of signals.
According to Ohler et al. [21], given a subsequence
si1 ¼ ðs1 ; s2 ; ; si Þ, conditional dependencies can be approximated by rational interpolation:
Pi1
ak gk ðsi1 ÞPbi ðsi jsi1 Þ
i1
P ðsi js1 Þ k¼0Pi1 ik i1 ik ;
ð4Þ
k¼0 ak gk ðsik Þ
where Pbi ðÞ denotes the empirical probability obtained from
Maximum Likelihood (ML) estimates from training data
sets, coefficient ak s denote real value coefficients such that
Pi1
k¼0 ak ¼ 1, and gk s denote functions that represent the
relationships of different-order contextual interactions
among variables sk , k ¼ 1; 2 . . . i [21].
By using the chain rule of probabilities, the likelihood of
the sequence sl1 is given by
P ðs1 ; s2 ; . . . sl Þ ¼ P ðs1 Þ
i
Y
P ðsi jsi1
1 Þ:
ð5Þ
i¼2
By induction of (4), that is, by replacing conditional
probabilities with the probabilities conditioned by a smaller
number of elements, we obtain
P ðs1 ; s2 ; . . . sl Þ P ðs1 Þ
l X
i1
Y
bij Pbi ðsi jsi1
ij Þ;
ð6Þ
i¼2 j¼1
where fbij : i ¼ 2; . . . l; j ¼ 1; . . . ig is a set of real numbers.
That is, the nonlinear relationship among variables in the
sequence is represented approximately by polynomials of
sufficient order.
As shown by Pinkus [28] and Hornik et al. [15], the
output of the neural network is capable of representing the
input-output relationship with a sufficiently large higherorder polynomial. Hence, the output of a neural network
receiving Markov probabilities Pi ðsi Þ, i ¼ 1; 2; . . . l, can be
written as
X
y¼
cm1 ;...ml P1 ðs1 Þm1 . . . Pl ðsl Þml ;
ð7Þ
m1 ;...ml ¼0;m1 þ...ml ¼l
where fmi ; i ¼ 1; 2; . . . lg is a set of nonnegative integers and
fcm1 ;...;ml ; m1 þ . . . ml ¼ lg is a set of real value coefficients.
By observation of (6) and (7), it can be deduced that the
neural network output, y, represents a higher-order Markov
model that takes care of all the conditional interactions
among all the nucleotides in the input sequence.
5
EXPERIMENTS
AND
RESULTS
In this section, we demonstrate the performance of our
approach, using experiments with benchmark data sets and
comparisons with earlier approaches. Experiments were
RAJAPAKSE AND HO: MARKOV ENCODING FOR DETECTING SIGNALS IN GENOMIC SEQUENCES
evaluated based on the standard performance measures:
sensitivity, specificity, precision, and accuracy.1 The sensitivity gives the percentage of correct prediction of true sites
and the specificity gives the percentage of correct prediction
of false sites. Whenever possible, we obtain Receiver
Operation Characteristics (ROC) plotting the sensitivity
values against one minus specificity at various threshold
values at the output of neural networks.
5.1 Training
The prediction models were trained in two phases: The
Markov chains’ parameters were estimated first and,
thereafter, the neural networks’ training was done. In order
to evaluate Markov model parameters, the corresponding
sequence segments were first aligned. The ML estimate of
the ith state of the k-order Markov model, say Pbi ðÞ, is given
by the ratios of the frequencies of all partial sequences of
k þ 1 elements at i and k elements at i 1 positions:
i
#ðsik Þ
;
Pbi ðsi Þ ¼
#ðsi1
ik Þ
ð8Þ
where #ðÞ represents the frequency of its argument in the
training data set.
In SS detection, for finding the parameters of the model
for true sites, the training sequences were aligned with
respect to the consensus di-nucleotide. The TATA-box and
Inr segments were extracted from the scanning window in
the TSS detection and the Markov model parameters were
estimated using the frequencies of nucleotides at each
position. In TIS detection, at each ATG site, 50 bp upstream
and 50 bp downstream (without ATG) were extracted,
resulting in 50 bp long sequences which may have flanking
N regions because of the lack of data in the upstream
context and/or downstream context of the ATG site.
Once the Markov chain parameters were learned, the
training sequences were again applied to the model and the
Markovian probabilities were used as inputs to neural
networks. Desired outputs were set to either 0.9 or 0.1 to
represent the true or false site at the output, correspondingly. In order to avoid overfitting, the number of the
hidden neurons was initially set such that the total number
of free parameters, i.e., the weights and biases, should be times the number of the training sequences, where denotes the fraction of detection errors permitted on testing
[13]. Starting from this configuration, the optimal number of
hidden neurons was then determined empirically.
For all the neural networks, the parameters of the
activation functions were ¼ 1:0, ¼ 1:716, and k ¼ 1:0
and k ¼ 1:0 for all k; we noticed that the performance
did not depend much on slight variations of these
parameter values. The standard online error backpropagation algorithm was used to train the neural networks [13]
with momentum initially set to 0:01 and learning rate
initially set to 0:1, for each hidden and output neuron,
and updated iteratively as in [19], [27]. The weights of
P
TN
TP
1. Sensitivity ¼ T PTþF
N , specificity ¼ T NþF P , precision ¼ T P þF P , and
P þT N
accuracy ¼ T P þTTNþF
P þF N , where TP, TN, FP, and FN denote the rates of
true positives, true negatives, false positives, and false negatives,
respectively [5], [37].
137
neural networks were initialized in [-1.0, 1.0] using the
Nguyen-Widrow method [20].
5.2 SS Detection
In this section, we compare the performance of our SS
detection method on two data sets: NN269 available at [46]
and GS1115 prepared by Pertea et al. [26]. In the case of
acceptor sites, a 189 bp window around the consensus dinucleotide (at the site) was used for all samples: 21 bp for
the intron (ending with AG) and 8 bp for the following
exon, i.e., lS ¼ 29, and two additional sequences of 80 bp,
i.e., lU ¼ lD ¼ 80. In the case of donor sites, a 176 bp
window around the consensus di-nucleotide (at the site)
was used for all samples, which has 6 bp of the exon and
10 bp of the following intron (starting with GT), lS ¼ 16, and
two additional sequences of 80 bp, i.e., lU ¼ lD ¼ 80. These
asymmetric configurations were selected because the most
conserved parts of the splicing signals extend more into the
intron regions [11].
The data set NN269, available at [46], provided by
Reese et al. [29] consists of 269 human genes. Confirmed
1,324 true acceptor sites and 1,324 true donor sites were
extracted from the data set. Additionally, 5,552 false
acceptor and 4,922 false donor sites with the consensus
GT or AG di-nucleotides appearing in a neighborhood of
plus and minus 40 nucleotides around a true splice site
were collected. Given the above numbers, we used the
empirical method, explained above to determine that five
hidden neurons were optimal for both donor and acceptor
networks.
Fig. 7 illustrates a comparison of the performance of the
present SS prediction with NNSplice [45] and GeneSplicer
[42], using the NN269 data set. We used the same experimental setup and data partitions that were used in the
experimentation of NNSplice [45]: The entire data set was
divided into a training set containing 1,116 true acceptor,
1,116 true donor, 4,672 false acceptor, and 4,140 false donor
sites, and a test set containing 208 true acceptor, 208 true
donor, 881 false acceptor, and 782 false donor sites. As seen,
the present approach showed more power in the detection of
splice sites than both the NNSplice and GeneSplicer.
Further, the SS prediction was tested using the data set
GS1115 prepared by Pertea et al. [26], using five-fold crossvalidation, to compare with the performance of GeneSplicer
[42], a method based on a Markov model. We used the same
data partions on GS1115 data set, used by GeneSplicer [42]:
Together with confirmed true 5,733 acceptor sites and 5,733
donor sites extracted from 1,115 human genes, 650,099 false
acceptor and 478,983 false donor sites, with confirmed GT
or AG di-nucleotides present and that are not annotated as
true sites, were collected. For this experiment, the neural
networks showed optimal performance with 15 hidden
neurons for the donor network and 30 hidden neurons for
the acceptor network. The performances of the present
approach with other previous techniques are given in Fig. 8.
Only the GeneSplicer program allows retraining the data set
and testing at various values of FN to obtain the complete
ROC curve. The performances of HSPL [44], SpliceView
[48], and GENIO [43] are only available at specific FN
values. As the publicly available NNSplice program does
138
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Fig. 7. Comparison of splice site (SS) detection by the present method, GeneSplicer, and NNSplice: ROC curves on the nonredundant 269 human
gene data set (NN269) for acceptor sites and donor sites.
Fig. 8. Comparison of performance of splice site (SS) detection with the GeneSplicer: ROC curves on the nonredundant 1,115 human gene data set
(GS1115) for acceptor sites and donor sites.
not allow retraining with new data sets, the comparison
with NNSplice is not presented.
Although the training of Markov chain models was in
real time, the training of the neural network was relatively
slow when there was a massive imbalance of the number of
true sites and false sites in the training data set. Therefore,
we selected a set of equal true and false ones, randomly in
every epoch, to train the neural network to improve the
training speed. A refinement step was performed in the
postprediction for further eliminating wrong predictions
and enhancing weak predictions, taking into consideration
1) the alternative positions of acceptors and donors [14],
2) the compositional differences between exons and introns
[6], and 3) the maximum and minimum lengths of introns
and internal exons [26].
Fig. 9 displays the probability distribution of the
nucleotides at specific positions in a representative upstream segment ½86; 7 and downstream segment
½þ11; þ90 of a true donor site represented by the secondorder Markov model and the die model (zero-order Markov
model) [2], assuming that the conserved GT di-nucleotide is
labeled ½þ1; þ2. The Markov models highlight the differences of positional probabilities of nucleotides better than
the die model, taking into consideration the neighborhood
dependencies such as codon distribution. Fig. 10 illustrates
how the Markov model captures the contrast between
upstream and downstream segments.
5.3 TSS Detection
In this study, the human promoter data set provided by
Reese [47] was used. The set essentially consists of three
parts: promoter sequences, CDS (coding) sequences, and
noncoding (intron) sequences. Each part contains five
sequence sets to be used for five-fold cross-validation. The
promoters were extracted from the Eukaryotic Promoter
Database (EPD) release 50 (575 sequences). Promoter entries
with less than 40 bp upstream and/or 5 bp downstream
were discarded, leaving 565 entries, out of which 250 bp
upstream and 50 bp downstream were extracted, resulting
in 300 bp long sequences which may have flanking
N regions due to the lack of data in the beginning and/or
end of the promoter region. The false set contains coding
and noncoding sequences from the 1998 GENIE data set
[47]. The exons were concatenated to form single CDS
sequences. The sequences were cut consecutively into 300 bp
long nonoverlapping sequences. The shorter and remaining
sequences at the end were discarded. Finally, 565 true
promoters, 890 CDS sequences, and 4,345 intron sequences
were included in the data set. The TATA neural network
showed optimal performance with seven hidden neurons,
RAJAPAKSE AND HO: MARKOV ENCODING FOR DETECTING SIGNALS IN GENOMIC SEQUENCES
139
Fig. 9. Illustration of Markov encoding in a representative (a) upstream and (b) downstream segment of a true donor site by comparing to positional
probabilities given by the die model.
Fig. 10. Illustration of the distribution of parameters of (a) die models and (b) Markov models in the region surrounding a true donor site.
the Inr neural network with seven hidden neurons, and the
concatenation of TATA and Inr network with 15 hidden
neurons. Following NNPP 2.1 method [30], we used TimeDelay Neural Networks (TDNN), which is a variant of MLP
whose hidden neurons activations are replicated over time
[13], for TATA neural network.
Fig. 11 shows a comparison of performance of the
detection of TSS between the present method using Markov
encoding and the NNPP 2.1 method, which uses a TDNN
receiving inputs from the concatenation of TATA and Inr
segments, with orthogonal encoding. As seen, the ROC
curves show the superiority of the present method over the
NNPP 2.1 technique on the tested data set. We further used
the standard correlation coefficient, r,2 to evaluate our
model. As seen in Table 1, the present method has a
correlation coefficient rate of 0.69, on average, which is
better than the rate 0.65 of NNPP 2.1.
5.4 TIS Detection
We used the data set provided by Pedersen and Nielsen for
training, testing, and evaluation of the TIS detection [24].
The set consists of sequences extracted from GenBank
2. The standard correlation coefficient [5]:
ðT P T NÞ ðF N F P Þ
r ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi :
ðT P þ F NÞ ðT N þ F P Þ ðT P þ F P Þ ðT N þ F NÞ
ð9Þ
release 95 and processed by removing introns and joining
the remaining exon parts. From the resulting sequences,
only those sequences containing at least 10 nucleotides
upstream and 150 nucleotides downstream (relative to the
A in the triplet ATG) were selected; all other sequences
were discarded. The sequences were filtered to remove the
redundancies because of the presence of genes belonging to
gene families, homologous genes from different organisms,
and sequences submitted to the database by more than one
source. In total, 13,375 ATG sites were included into the
data set, of which there are 3,312 true TISs and 10,063 false
TISs. Of the false TISs, 2,077 are upstream of true TISs. The
data set was split into three equal-sized subsets and used
for three-fold cross-validation. For optimal performance, we
empirically found five hidden neurons for the upstream
neural network, seven hidden neurons for the downstream
neural network, and 20 hidden neurons for the consensus
neural network.
The performance comparisons between the present
method and previous TIS recognition systems [12], [24],
[18], [41] are illustrated in Table 2. The version of the datamining program proposed in [18] used in this comparison
was equipped with the ribosome scanning model. The result
reported by Hatzigeorgiou [12] was not directly comparable
since she used a different data set. As seen, the present
method achieved an average 93.8 percent of sensitivity and
96.9 percent of specificity, compared to the previously
reported best 88.5 percent of sensitivity and 96.3 percent of
specificity by the data mining-based program [18].
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VOL. 2,
NO. 2,
APRIL-JUNE 2005
TABLE 2
Comparison of Average Results with Three-Fold
Cross-Validation of the Present Method with
Previous TIS Recognition Methods
Character “-” indicates that the values were not reported in the literature.
Fig. 11. Comparison of transcription start site (TSS) prediction between
the present method and the NNPP 2.1 method.
6
CONCLUSION
We presented a Markov/neural hybrid approach to detect
signals, such as SS, TSS, and TIS, in genomic sequences. The
approach used Markov encoding: The inputs to the neural
networks are Markovian probabilities that characterize the
prior biological knowledge on coding and noncoding
regions. The neural networks capture intrinsic features
surrounding the signals by combining lower-order Markovian probabilities and finding an appropriate arbitrary
mapping that represents the signal accurately. As shown,
the present hybrid model effectively implements a complex
higher-order Markov model. Although the higher-order
Markov models were often touted earlier as accurate
models to characterize signals [18], their direct implementation has been practically prohibitive because of the need for
estimating the large number of parameters with the often
limited amount of training data.
The lower-order Markov models incorporate useful
biological knowledge such as the bias of codon distributions, the contrast between exons and introns, and the
homology of potential signal sites. However, these models
are incapable of representing more complex nonlinear
interactions among nucleotides surrounding the signal
sites, which may be useful for their identification. Neural
networks, being large nonparametric nonlinear models, are
TABLE 1
Comparison of Correlation Coefficients, Averaged
over Five-Fold Cross-Validated Sets between the
Present Neural Network Method and NNPP 2.1 Method
Notation “-” indicates that NNPP 2.1 was unable to achieve 90 percent
true positives.
capable of finding complex mapping through learning. In
the present approach, the neural networks nonlinearly
combine lower-order interactions, represented by Markov
probabilities, to realize the higher-order distant interactions
among nucleotides. Not only the lower-order Markov
models, our method can be extended for other models to
represent biological knowledge, such as the protein encoding model used in TIS prediction. Further, the Markov
encoding scheme can be used as a preprocessing step for
the inputs to the other detection techniques using Support
Vector Machines, decision trees, etc., and, in principle,
should improve their performances.
The tenet of any approach of signal detection is to first
discover relevant biological features and then process them
optimally for correct prediction with high sensitivity and
specificity. The present method allows both incorporation
of biological knowledge and learning of intrinsic complex
features. Neural networks have been used earlier for
prediction of signals with orthogonal coding [4], [11], [29],
which did not allow the incorporation of prior knowledge.
As demonstrated in the experiments, with the incorporation
of explicit biological features, using the Markov models at
the input, the accuracies of prediction of signals by the
neural networks improved. Also, the present method
outperformed the methods that use only Markov models,
such as the GeneSplicer used in SS detection, as they are
unable to capture more complex features resulting from
nonlinear and distant interactions of nucleotides, and the
pure neural network approaches, such as the NNPP 2.1
method in TIS detection, that use orthogonal encoding.
Our comparisons to the existing techniques were,
however, limited due to the inaccessibility to the programs
and the previously used data. On the different data sets
with different characteristics, e.g., the proportion of true
and false sites, the techniques gave different results.
Nevertheless, the present method outperformed earlier
approaches on the tested data sets, supporting that the
proposed Markov/neural models can potentially model
signals in genomic sequences, as illustrated by the detection
of SS, TIS, and TSS. The parameters determined for neural
network configurations and training might not be optimal,
though our testing focused on investigating the effectiveness of Markov encoding method. As for the length of
segments of signal models, we relied on previously
reported values in the literature. Our future work involves
investigation into the selection of the length of segments
representing different signals under the present framework.
RAJAPAKSE AND HO: MARKOV ENCODING FOR DETECTING SIGNALS IN GENOMIC SEQUENCES
In conclusion, we proposed using lower-order Markov
models for encoding the input sequences for the prediction
of signals by neural networks and demonstrated the
efficacy of the Markov/neural approach in the detection
of three signals, namely, SS, TIS, and TSS. The present
model is capable of implementing higher-order Markov
models of the signal sites and provides an efficient and
feasible method of learning model parameters, leading to
better detection of the signals.
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142
IEEE/ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS,
Jagath C. Rajapakse received the BSc (engineering) degree with first class honors from the
University of Moratuwa (Sri Lanka) in 1985. He
won the award for the best undergraduate in
electronic and telecommunication engineering
and also received the Fulbright scholarship
(1987-1989). He received the MSc and PhD
degrees in electrical and computer engineering
from the State University of New York at Buffalo
in 1989 and 1993, respectively. He was a visiting
fellow at the National Institutes of Health (Bethesda) from 1993-1996
and then a visiting scientist at the Max-Planck-Institute of Cognitive
Neuroscience (Leipzig, Germany). In May 1998, he joined Nanyang
Technological University (Singapore), where he is presently an
associate professor in the School of Computer Engineering and also
the Deputy Director of the BioInformatics Research Centre (BIRC). He
has authored more than 150 research publications in refereed journals,
conference proceedings, and books. He also serves on the editorial
boards of the journals Neural Information Processing: Letters and
Reviews and the International Journal of Computational Intelligence. He
is a senior member of the IEEE, a governing board member of APNNA,
and a member of AAAS. His current teaching and research interests are
in computational biology, neuroimaging, and machine learning.
VOL. 2,
NO. 2,
APRIL-JUNE 2005
Loi Sy Ho received the BS degree with first
class honors in computer science from Vietnam
National University, Hanoi, in 2000. Since July
2001, he has been a PhD student in the School
of Computer Engineering, Nanyang Technological University, Singapore. His research has
been in the area of bioinformatics, including
computational techniques to detect various
signals and structures in biological sequences.
He has published more than 10 research
papers. Ho has received the Best Student Paper Award and the Overall
Best Paper Award at the First IEEE Symposium on Computational
Intelligence in Bioinformatics and Computational Biology (CBICB 2004).
He was also awarded the Young Scientist Award by the Japanese
Society for Bioinformatics for the work he presented at the 14th
International Conference on Genomic Informatics (GIW 2003).
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